Question

$P(A-B)=P\left(A\right)-P(A\bigcap B)=P(A\bigcup B)-P\left(B\right)=P(A\bigcap \overline{B})=1-P(\overline{A}\bigcap B)$

• A. True
• B. False

Answer 1

The correct option is A True

P(A-B) is shown blue shaded region

P(A)−P(A⋂B) is again shown in the blue region

P(A⋃B)−P(B)=P(A)+P(B)-P(A⋂B)-P(B)

=P(A)−P(A⋂B)

P(A⋂B¯)=P(A⋃B)−P(B)

Also $P(A\cap \stackrel{\_}{B})+P(\stackrel{\_}{A}\cap B)=1\Rightarrow P(A\cap \stackrel{\_}{B})=1-P(\stackrel{\_}{A}\cap B)$